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k0ka [10]
3 years ago
7

Write a proportion that could be used to solve for each variable. Then solve.

Mathematics
1 answer:
iren [92.7K]3 years ago
4 0
60/25 = 12/Y
cross multiply and divide

25 x 12 = 300 

300 / 60 = 5

Y = 5 boxes
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Evaluate the definite integral using the graph of f(x)<br> (Image included)
Tanya [424]

a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

\displaystyle \int_0^3 f(x) \, dx = \frac12 \times 3 \times 5 = \boxed{\frac{15}2}

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

\displaystyle \int_3^5 f(x) \, dx = \int_3^4 f(x) \, dx + \int_4^5 f(x) \, dx = \int_3^4 f(x) \, dx - \int_3^4 f(x) \, dx = \boxed{0}

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

\displaystyle \int_5^9 f(x) \, dx = -4\times5 = -20

Then by linearity, we have

\displaystyle \int_0^9 f(x) \, dx = \left\{\int_0^3 + \int_3^5 + \int_5^9\right\} f(x) \, dx = \frac{15}2 + 0 - 20 = \boxed{-\frac{25}2}

8 0
2 years ago
It’s a yes or no question<br> !!!!!!!!!!!!<br> For math
vesna_86 [32]
I’m confused on what the question is exactly
5 0
3 years ago
-3, 6, -9, 12, -15, . . .
Nataly_w [17]
The second one is right
8 0
3 years ago
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GEOMETRY HELPP -- WILL MARK BRAINLIEST
lukranit [14]

Answer: d = 29 miles

Step-by-step explanation:

S11°W  = 259° on a unit circle

N75°E = 15° on a unit circle

x separation after two hours

x = 2(8cos15 - 18cos259) = 21.179 miles

y separation after two hours

x = 2(8sin15 - 18sin259) = 19.7398 miles

total distance between them is

d = √(19.7398² + 21.179²) = 28.9518... ≈ 29 miles

3 0
3 years ago
What is the solution to this equation x+6=24
mihalych1998 [28]

x=18 if im not mistaken that was pretty easY

3 0
3 years ago
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