Answer:
24/30 is
Step-by-step explanation:
0.8
g A spotlight on the ground is shining on a wall 20m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 0.8m/s, how fast is the length of her shadow on the building decreasing when she is 4m from the building
Answer:
0.3 m/s
Step-by-step explanation:
[tex]\dfrac{dx}{dt}=\text{Speed of person}=0.8\ \text{m/s}[/tex]
As the two triangles in the diagram are similar to each other we have
[tex]\dfrac{y}{12}=\dfrac{2}{8}\\\Rightarrow y=12\times \dfrac{2}{8}\\\Rightarrow y=3\ \text{m}[/tex]
Again as the triangles are similar we have
[tex]\dfrac{y}{2}=\dfrac{12}{12-x}\\\Rightarrow x=12-\dfrac{24}{y}[/tex]
Differentiating the above equation with respect to time we get
[tex]\dfrac{dx}{dt}=\dfrac{-24\times-1}{y^2}\dfrac{dy}{dt}\\\Rightarrow \dfrac{dy}{dt}=\dfrac{dx}{dt}\times\dfrac{y^2}{24}\\\Rightarrow \dfrac{dy}{dt}=0.8\times \dfrac{3^2}{24}\\\Rightarrow \dfrac{dy}{dt}=0.3\ \text{m/s}[/tex]
The speed at which the shadow is changing is 0.3 m/s.
Five less than twice a number is ten
Nine
“five less” than “twice a” number is “nine”.p-by-step explanation:
A conical water tank with vertex down has a radius of 11 feet at the top and is 20 feet high. If water flows into the tank at a rate of 10 ft3/minft3/min, how fast is the depth of the water increasing when the water is 12 feet deep?
Answer:
0.073 ft/min
Step-by-step explanation:
The radius of the tank = 11 feet and the height of the tank = 20 feet. The depth of water = h = 12 feet, let r be the radius of the water, hence:
[tex]\frac{r}{h}=\frac{11}{20}\\ \\r=\frac{11}{20}h\\ \\The \ volume\ of\ the \ tank\ is:\\\\V = \frac{1}{3} \pi r^2 h=\frac{1}{3}\pi (\frac{11}{20}h)^2.h=\frac{121}{1200}\pi h^3 \\\\Given\ that\ rate=\frac{d}{dt}(V)= 10ft^3/min\\\\\frac{dV}{dt}= \frac{d}{dt}( \frac{121}{1200}\pi h^3)\\\\\frac{dV}{dt}=\frac{121}{1200}\pi (3h^2\frac{dh}{dt})\\\\\frac{dV}{dt}=\frac{121}{400}\pi h^2(\frac{dh}{dt})\\\\Given\ water\ is\ 12ft\ deep, i.e.\ h=12.Substituting:\\\\[/tex]
[tex]10=\frac{121}{400}\pi (12^2)\frac{dh}{dt} \\\\\frac{dh}{dt} =0.073\ ft/min[/tex]
Find equation with points (-3,-8) and (1, 16)
Answer:
The equation of the line is y = 6x + 10.
Step-by-step explanation:
(-3,-8) (1 ,16)
x1, y1. x2,y2
Gradient(m) = (y2 - y1)/(x2 - x1)
= (16 - (-8))/(1 - (-3))
= 24/4 = 6
Equation of a line is given as:
(y - y1) = m(x - x1)
y - (-8) = 6(x - (-3))
y + 8 = 6x + 18
y = 6x + 10
Kelly needs to buy 5 notebooks and 3 folders for school. If notebooks cost $6 and folders cost $2, how much money does Kelly need for school supplies?
Answer:
$36
Step-by-step explanation:
How many solutions does 49m+9=49m+83 have
None. You cancel out 49m on both sides and get 9 = 83, that is not true so there aren't any solutions.
Solve:
12 x 1/2=
1/2 x 18 =
Step-by-step explanation:
12*1/2 = 6
1/3 * 18 =9
Hope this helps
how many gallons is in 152 cups
Answer:
9.5
Step-by-step explanation:
You're welcome have a nice
If the absolute value of the correlation is approximately one, then the points lie close to a line that slopes upward or downward?
Answer:
if it is positive then it goes upward and if negative it goes downward..so if it is approximately 1 then it will be constant or straight...
If six pieces come off of a hot press, find the probability that two are Grade A, three are Grade B, and one is a Cull.
Step-by-step explanation:
Given data:
No of pieces = 6
Grade A = 2
Grade B = 3
Cull = 1.
Solution:
Probability that two are Grade A
P = 2/6
= 0.33
Probability that 3 are Grade B
P = 3/6
= 0.5
Probability that 1 is a cull
P = 1/6
= 0.17
If ĐPQR = 50°, what is the measure of its complement?
Answer:
The measure of its complement is 40°
Step-by-step explanation:
The sum of the measures of the complementary angles is 90°If the measure of an angle is x°, then the measure of its complement is 90° - x°∵ The measure of angle PQR equal 50 degrees
∴ m∠PQR = 50°
∵ Angle x is the complement angle of angle PQR
→ That means the sum of the measures of angle x and angle PQR is 90°
∴ m∠x + m∠PQR = 90
→ Substitute measure of angle PQR by 50°
∴ m∠x + 50 = 90
→ Subtract 50 from both sides
∴ m∠x + 50 - 50 = 90 - 50
∴ m∠x = 40°
∴ The measure of its complement is 40°
Can someone help me with this
Answer:
2 1/8 = h
2 1/2 = k
2 5/8 = L
1 7/8 = g
1 5/8 = e
2 3/4 = m
1 1/2 = d
2 1/4 = I
1 3/8 = c
2 7/8 = n
1 1/8 = a
Step-by-step explanation:
2) Michelle was 3 miles from home. 2 hours later, she was 15 miles from home.
What is her speed?
help me pleaseeeeeeee
Answer:
gladly
Step-by-step explanation:
Mount Whitney is 3072m tall. Convert the height to kilometers.
Help me
I will mark is the most brilliant answer
Answer:
Number one is D/12.5
Step-by-step explanation:
correct me if im wrong plz
Factor the polynomial function over the complex numbers.
f(x)=x4−x3−2x−4
Enter your answer in the box.
f(x)=
Answer:
2Step-by-step explanation:
Given function
f(x)=x⁴−x³−2x−4Factoring the polynomial
x⁴−x³−2x−4 = (x⁴−4) − (x³+2x) =(x² + 2)(x² - 2) - x(x² + 2) =(x² + 2)(x² - x - 2) =(x + i√2)(x - i√2)(x - 2)(x + 1)As we see there are 2 complex factors
Answer:
(x+1)(x-2)(x+i√2)(x-i√2)
Step-by-step explanation:
There were 600 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1,160.
How many adults and how many children attended? Use the elimination method.
A. 290 adults and 310 children
B. 160 adults and 440 children
C. 320 adults and 280 children
D. 280 adults and 320 children
Determine if the rates are equivalent.explain your reasoning 25 hours in 5 days 8 hours in 2 days
Answer:
No they are not equal
Step-by-step explanation:
25/5 and 8/2 are not equal 25/5 is equal to 5 and 8/2 is equal to 4.
Hope this helps☺️
t is no more than 2 units from 9
Answer:
11 or 7
Step-by-step explanation:
9 + 2 = 11
9 - 2 = 7
3.7 x 10 to the power of 6 written in decimal form
Answer:
3,700,000
Step-by-step explanation:
What is
Solve 5(x+4)<75
Answer:
x < 11
Step-by-step explanation:
5 (x + 4) < 75
5 (x + 4)/5 < 75/5
x +4 < 15
x + 4 - 4 < 15 - 4
x < 11
You must be at least 48 inches tall to ride an amusement park ride, and your little sister is 39 inches tall. How
many inches i must she grow before she may ride the ride?
Whats the inequality ?
Answer:
9
Step-by-step explanation:
48-39=9
Answer:
9
Step-by-step explanation:
person above me is correct
An item on sale costs 40% of the original price. If the original price was $75, what is the sale price?
Answer:
$45
Step-by-step explanation:
75 * 0.40= 30
75-30= 45
i don’t have timeee plsss hurry!
Answer:
there is no remainder but its 11
Answer:
Quotient is 11 and the remainder is 0
Step-by-step explanation: 143÷13 is 11 so therefore there would be no remainder :)
find the value of
sin 0.4
Answer:
In radians: 0.3894
In degrees: 0.00698
Step-by-step explanation:
Plug it into a calculator.
Can somebody answer this Asp please
Answer:
the answer is the third one C
Jane earns $280 per week. Of her salary, 231% goes to taxes. After taxes, she puts 50% in savings and keeps 50% for spending. Of her
spending money, she uses 35% for food. About how much money does Jane spend on food each week?
A $26.22
B. $19.60
C. $23.10
D. $37.61
Answer:
i think its A. or D.
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
0.2325 times 280 is 65.1
280-65.1
214.9
214.9 divided by 2
107.45
107.45 times 0.35
37.6075 rounded to 37.61
5/6%1/3 math question
Answer:
0.277(continued)
Step-by-step explanation:
estimate the product choose a method 63 * 18
Answer:
[tex]the \: product : 63 * 18 = 63 \times18 \\ 63 * 18 = 1,134.[/tex]
